1. Field of the Invention
The present invention relates to orthogonal frequency division multiplexing (OFDM) and particularly to an OFDM receiver with a channel estimator using 2-dimensional interpolation.
2. Description of the Prior Art
OFDM is a multi-channel modulation system employing Frequency Division Multiplexing (FDM) of orthogonal sub-carriers, each modulating a low bit-rate digital stream.
In older multi-channel systems using FDM, the total available bandwidth is divided into N non-overlapping frequency sub-channels. Each sub-channel is modulated with a separate symbol stream and the N sub-channels are frequency multiplexed. Even though the prevention of spectral overlapping of sub-carriers reduces (or eliminates) Inter-channel Interference, this leads to an inefficient use of spectrum. The guard bands on either side of each sub-channel waste precious bandwidth. To overcome the problem of bandwidth wastage, alternatively, N overlapping (but orthogonal) sub-carriers, each carrying a baud rate of 1/T and spaced 1/T apart can be used. Because of the frequency spacing selected, the sub-carriers are all mathematically orthogonal to each other. This permits the proper demodulation of the symbol streams without requiring non-overlapping spectra. Another way of specifying the sub-carrier orthogonality is to require that each sub-carrier have an exact integer number of cycles in the interval T. The modulation of these orthogonal sub-carriers can be represented as an Inverse Fourier Transform. Alternatively, a DFT operation followed by low-pass filtering can generate the OFDM signal. It must be noted that OFDM can be used either as a modulation or multiplexing technique.
The use of Discrete Fourier Transform (DFT) in the parallel transmission of data using Frequency Division Multiplexing was investigated in 1971 by Weinstein and Ebert. In a data sequence d0, d2, . . . , dN−1, where each dn is a complex symbol (the data sequence can be the output of a complex digital modulator, such as QAM, PSK etc), when performing an IDFT on the sequence 2dn (the factor 2 is used purely for scaling purposes), N complex numbers Sm (m=0,1 . . . , N−1) result, as:
                              S          m                =                              2            ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                d                  n                                ⁢                                  exp                  ⁡                                      (                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                        n                          ⁢                                                                                                          ⁢                          m                                                N                                                              )                                                                                ⁢                                          ⁢                                          =                      2            ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                d                  n                                ⁢                                                      exp                    ⁡                                          (                                              j                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          n                                                ⁢                                                  t                          m                                                                    )                                                        ⁢                                                                          [                                                            m                      =                      0                                        ,                    1                    ,                                                                                  ⁢                                                                  …                        ⁢                                                                                                  ⁢                        N                                            -                      1                                                        ]                                                                                        (        2.1        )            Where,
                              f          n                =                                            n                              N                ⁢                                                                  ⁢                                  T                  s                                                      ⁢                                                  ⁢            and            ⁢                                                  ⁢                          t              m                                =                      m            ⁢                                                  ⁢                          T              s                                                          (        2.2        )            Where, Ts represents the symbol interval of the original symbols. Passing the real part of the symbol sequence represented by equation (2.1) thorough a low-pass filter with each symbol separated by a duration of Ts seconds, yields the signal,
                                          y            ⁡                          (              t              )                                =                      2            ⁢                                                  ⁢            Re            ⁢                          {                                                ∑                                      n                    =                    0                                                        N                    -                    1                                                  ⁢                                                      d                    n                                    ⁢                                      exp                    ⁡                                          (                                              j                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                              n                            ⁢                                                                                                                                          T                                                ⁢                        t                                            )                                                                                  }                                      ,                              for            ⁢                                                  ⁢            0                    ≦          t          ≦          T                                    (        2.3        )            Where T is defined as NTs. The signal y(t) represents the baseband version of the OFDM signal.
It can be noted from (2.3) that the length of the OFDM signal is T, the spacing between the carriers is equal to 1/T, the OFDM symbol-rate is N times the original baud rate, there are N orthogonal sub-carriers in the system, and the signal defined in equation (2.3) is the basic OFDM symbol.
One of the main advantages of OFDM is its effectiveness against the multi-path delay spread frequently encountered in mobile communication channels. The reduction of the symbol rate by N times results in a proportional reduction of the relative multi-path delay spread, relative to the symbol time. To completely eliminate even the very small ISI that results, a guard time is introduced for each OFDM symbol. The guard time must be chosen to be larger than the expected delay spread, such that multi-path components from one symbol cannot interfere with the next symbol. Leaving the guard time empty may lead to inter-carrier interference (ICI), since the carriers are no longer orthogonal to each other. To avoid such crosstalk between sub-carriers, the OFDM symbol is cyclically extended in the guard time. This ensures that the delayed replicas of the OFDM symbols always have an integer number of cycles within the FFT interval as long as the multi-path delay spread is less than the guard time.
If the ODFM symbol is generated using equation (2.3), the power spectral density of this signal is similar to that shown in FIG. 4. The sharp-phase transitions caused by phase modulation result in very large side-lobes in the PSD and the spectrum falls off rather slowly (according to a sinc function). If the number of sub-carriers increases, the spectrum roll-off is sharper in the beginning, but moves further away at frequencies from the 3-dB cut-off frequency. To overcome this problem of slow spectrum roll-off, a windowing may be used to reduce the side-lobe level. The most commonly used window is the Raised Cosine Window given by:
      w    ⁡          (      t      )        =      {                                                      0.5              +                              0.5                ⁢                                  cos                  ⁡                                      (                                          π                      +                                              π                        ⁢                                                                                                  ⁢                                                  t                          /                                                      (                                                          β                              ⁢                                                                                                                          ⁢                                                              T                                r                                                                                      )                                                                                                                )                                                                        ,                                                  ⁢                                          …                ⁢                                                                  ⁢                0                            ≤              t              ≤                              β                ⁢                                                                  ⁢                                  T                  r                                                                                                      1.0            ,                                                  ⁢                                          …                ⁢                                                                  ⁢                β                ⁢                                                                  ⁢                                  T                  r                                            ⁢                                                          ≤              t              ≤                              T                r                                                                                                                    0.5                +                                  0.5                  ⁢                                      cos                    ⁡                                          (                                                                        (                                                      t                            -                                                          T                              r                                                                                )                                                ⁢                                                  π                          /                          β                                                ⁢                                                                                                  ⁢                                                  T                          r                                                                    )                                                                                  )                        ,                                                  ⁢                                          …                ⁢                                                                  ⁢                                  T                  r                                            ≤              t              ≤                                                (                                      1                    +                    β                                    )                                ⁢                                  T                  r                                                                        
Here Tr is the symbol interval chosen to be shorter than the actual OFDM symbol duration, since the symbols are allowed to partially overlap in the roll-off region of the raised cosine window. Incorporating the windowing effect, the OFDM symbol can now be represented as:
            y      ⁡              (        t        )              =          2      ⁢                          ⁢      Re      ⁢              {                              w            ⁡                          (              t              )                                ⁢                                    ∑                              n                =                0                                            N                -                1                                      ⁢                                          d                n                            ⁢                              exp                ⁡                                  (                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                  n                        ⁢                                                                                                                      T                                        ⁢                    t                                    )                                                                    }              ,            for      ⁢                          ⁢      0        ≦    t    ≦    T  
It must be noted that filtering can also be used as a substitute for windowing, for tailoring the spectrum roll-off. Windowing, though, is preferred to filtering because it can be carefully controlled. With filtering, rippling effects in the roll-off region of the OFDM symbol must be avoided. Rippling causes distortions in the OFDM symbol, which directly leads to less-delay spread tolerance.
Based on the previous discussions, the method for generating an ODFM symbol is as follows.
First, the Ns input complex symbols are padded with zeros to get N symbols to calculate the IFFT. The output of the IFFT is the basic OFDM symbol.
Based on the delay spread of the multi-path channel, a specific guard-time must be chosen (e.g. Tg). A number of samples corresponding to this guard time must be taken from the beginning of the OFDM symbol and appended to the end of the symbol. Likewise, the same number of samples must be taken from the end of the OFDM symbol and inserted at the beginning.
The OFDM symbol must be multiplied by the raised cosine window to remove the power of the out-of-band sub-carriers.
The windowed OFDM symbol is then added to the output of the previous OFDM symbol with a delay of Tr, so that there is an overlap region of βTr between each symbol.
OFDM system design, as in any other system design, involves tradeoff and conflicting requirements. The following are the most important design parameters of an OFDM system and may form part of a general OFDM system specification: Bit Rate required for the system, Bandwidth available, BER requirements (Power efficiency) and RMS delay spread of the channel.
Guard Time
Guard time in an OFDM system usually results in an SNR loss in an OFDM system, since it carries no information. The choice of the guard time is straightforward once the multi-path delay spread is known. As a rule of thumb, the guard time must be at least 2-4 times the RMS delay spread of the multi-path channel. Further, higher-order modulation schemes (like 32 or 64 QAM) are more sensitive to ISI and ICI than simple schemes like QPSK. This factor must also be taken into account when determining the guard-time.
Symbol Duration
To minimize SNR loss due to guard time, symbol duration must be set much higher than guard time. An increase in symbol time, however, implies a corresponding increase in the number of sub-carriers and thus an increase in the system complexity. A practical design choice for symbol time requires at least five times the guard time, which leads to an acceptable SNR loss.
Number of Sub-Carriers
Once the symbol duration is determined, the number of sub-carriers required can be determined by first calculating the sub-carrier spacing buy simply inverting the symbol time (less the guard period). The number of sub-carriers is the available bandwidth divided by the sub-carrier spacing.
Modulation and Coding Choices
The first step in selecting coding and modulation techniques is to determine the number of bits carried by an OFDM symbol. Then, a suitable combination of modulation and coding techniques can be selected to fit the input data rate into the OFDM symbols and, at the same time, satisfying the bit-error rate requirements. Selection of modulation and coding techniques is now simplified, since each channel is assumed to almost AWGN and there is no requirement for consideration of the effects of multi-path delay spread.
OFDM possesses inherent advantages for wireless communications.
As discussed earlier, the increase in the symbol time of the OFDM symbol by N times (N being the number of sub-carriers), leads to a corresponding increase in the effectiveness of OFDM against the ISI caused due to multi-path delay spread. Further, use of the cyclic extension process and proper design can completely eliminate ISI from the system.
In addition to delay variations in the channel, the lack of amplitude flatness in the frequency response of the channel also causes ISI in digital communication systems. A typical example would be twister-pair cable use in telephone lines. These transmission lines handle voice calls and have a poor frequency response when it comes to high frequency transmission. In systems that use single-carrier transmission, an equalizer may be required to mitigate the effect of channel distortion. The complexity of the equalizer depends upon the severity of the channel distortion and there are frequently issues such as equalizer non-linearities and error propagation etc., that cause additional trouble.
In OFDM systems, on the other hand, since the bandwidth of each sub-carrier is very small, the amplitude response over this narrow bandwidth will be basically flat (of course, it can be safely assumed that the phase response will be linear over this narrow bandwidth). Even in the case of extreme amplitude distortion, an equalizer of very simple structure will be enough to correct the distortion in each sub-carrier.
The use of sub-carrier modulation improves the flexibility of OFDM to channel fading and distortion makes it possible for the system to transmit at maximum possible capacity using the technique of channel loading. If the transmission channel has a fading notch in a certain frequency range corresponding to a certain sub-carrier, the presence of this notch can be detected using channel estimation schemes, and assuming that the notch does not vary fast enough compared to the symbol duration of the OFDM symbol, it is possible to change (scale down/up) the modulation and coding schemes for this particular sub-carrier (i.e., increase their robustness against noise), so that capacity as a whole is maximized over all the sub-carriers. However, this requires the data from channel-estimation algorithms. In the case of single-carrier systems, nothing can be performed against such fading notches. They must somehow survive the distortion using error correction coding or equalizers.
Impulse noise usually comprises a burst of interference in channels such as the return path HFC (Hybrid-Fiber-Coaxial), twisted-pair and wireless channels affected by atmospheric phenomena such as lightning etc. It is common for the length of the interference waveform to exceed the symbol duration of a typical digital communication system. For example, in a 10 MBPS system, the symbol duration is 0.1 μs, and an impulse noise waveform, lasting for a couple of micro-seconds, can cause a burst of errors that cannot be corrected using normal error-correction coding. Usually complicated Reed-Solomon codes in conjunction with huge interleaves are used to correct this problem. OFDM systems are inherently robust against impulse noise, since the symbol duration of an OFDM signal is much larger than that of the corresponding single-carrier system and thus, it is less likely that impulse noise will cause (even single) symbol errors. Thus, complicated error-control coding and interleaving schemes for handling burst-type errors are not really required for OFDM Systems simplifying the transceiver design.
OFDM is the best environment in which to employ frequency diversity. In fact, in a combination of OFDM and CDMA, called MC-CDMA transmission, frequency diversity is inherently present in the system (i.e., it is freely available). Even though OFDM provides advantages for wireless transmission, it has a few serious disadvantages that must be overcome for this technology to become a success.
Many applications that use OFDM technology have arisen in the last few years. In the following, one such application, DVB-T, is described in detail.
Digital Video Broadcasting (DVB) is a standard for broadcasting Digital Television over satellite, cable, and terrestrial (wireless) transmission.
DVB-T has two modes of operation, a 2 k mode with 1705 sub-carriers and 8 k modes with 6817 sub-carriers. DVB-T uses QPSK, 16-QAM or 64-QAM mapping for modulation, and uses a Reed-Solomon outer code (204, 188, t=8) and an outer convolutional interleaving. Besides, an inner convolutional code with generator polynomials (171,133 octal) combined with two layers of interleaving for error-control is used. Such OFDM system with coding also names as COFDM. Finally, pilot sub-carriers obtain reference amplitudes and phases for coherent demodulation. Two-dimensional channel estimation is performed using the pilot sub-carriers, which aids in the mobile reception of the OFDM signal.
The 2 k mode is suitable for single-transmitter operation and for relatively small single-frequency networks with limited transmitter power. The 8 k mode can be used both for single-transmitter operation and for large-area single-frequency networks.
Improved multi-path immunity is obtained through the use of a guard interval, a portion of the digital signal given away for echo resistance. This guard interval, which length is selectable, reduces the transmission capacity of OFDM systems. However, the greater the number of OFDM carriers provided, for a given maximum echo time delay, the less transmission capacity is lost. Nonetheless, a tradeoff is involved. Simply increasing the number of carriers has a significantly detrimental impact on receiver complexity and phase-noise sensitivity.
Because of the multi-path immunity of OFDM, it may be possible to operate an overlapping network of transmitting stations with a single frequency. In the areas of overlap, the weaker of the two received signals is similar to an echo signal. However, if the two transmitters are far apart, causing a large time delay between the two signals, the system will require a large guard interval.
The potential exists for three different operating environments for digital terrestrial television in Europe, including broadcast on a currently unused channel, such as an adjacent channel, or on a clear channel; broadcast in a small-area single-frequency network (SFN); or broadcast in a large-area SFN.
One of the main challenges for the DVB-T developers is that the different operating environments lead to somewhat different optimum OFDM systems. The common 2 k/8 k specification has been developed to offer solutions for all (or nearly all) operating environments.
As previously described, in the OFDM receiver to which the present invention particularly relates, a dynamic estimation of channel is necessary before the demodulation of OFDM signals since the radio channel is frequency selective and time-variant for wideband mobile communication systems.
The channel estimation can be performed by either inserting pilot tones into all of the sub-carriers of OFDM symbols with a specific period or inserting pilot tones into each OFDM symbol. The first method, block type pilot channel estimation, has been developed under the assumption of slow fading channel. Even with decision feedback equalizer, this assumes that the channel transfer function does not change very rapidly. The estimation of the channel for this block-type pilot arrangement can be based on Least Square (LS) or Minimum Mean-Square (MMSE). The MMSE estimate has been shown to give 10-15 dB gain in signal-to-noise ratio (SNR) for the same mean square error of channel estimation over LS estimate. The second, the comb-type pilot channel estimation, has been introduced to satisfy the need for equalizing when the channel changes even from one OFDM block to the subsequent block. The comb-type pilot channel estimation consists of algorithms to estimate the channel at pilot frequencies and to interpolate the channel.
U.S. Pat. No. 6,298,035 discloses a method and apparatus for estimating separate channel frequency responses for two channels in an orthogonal frequency division multiplexing system with two transmitters. The channel frequency responses are estimated using specifically selected training symbols that are broadcast from the two transmitters. The training symbols are specifically selected so as to improve the estimation of the channel frequency responses for each channel, while requiring the same amount of training symbols as in an estimation of the channel frequency response of a single channel.
U.S. Pat. No. 6,473,393 discloses channel estimation for OFDM systems with transmitter diversity. In a receiver that includes a plurality of receiving antennas that supply signals to associated OFDM receiving modules, and the receiving modules provide signals that are applied to a detector, channel parameters needed for proper detection are estimated during normal operation, in addition to an initial estimate based on a known training sequence. In computing the channel impulse response estimates between the signal received at that receiving antenna and the various transmitting antennas, an nK0×nK0 matrix of terms (qxy [1]) is developed. The inverse of the matrix is then computed, and the computed matrix inverse is multiplied by a vector of terms (pi [1]), to obtain a vector of nK0-sample channel impulse response estimates.
U.S. Pat. No. 6,487,253 discloses systems and methods for estimating channel response in the presence of interference. Interference and/or noise present on received training symbols is estimated. Based on the measured noise and/or interference, a weighting among training symbols is developed. Channel response is then estimated based on a weighted least squares procedure.
However, the estimation methods described previously are 1-dimensional. That is to say, the channels are estimated by interpolation between pilots only in frequency domain. The channels are time-varied as well as frequency selective. The 1-D interpolation in frequency domain does not reflect the variety of the channels in time domain. An OFDM receiver with a 1-dimensional channel estimator is not suitable for mobile reception.